1 % Time Series Analysis (Ver 3.10)
2 % Schloegl A. (1996-2003,2008) Time Series Analysis - A Toolbox for the use with Matlab.
3 % WWW: http://hci.tugraz.at/~schloegl/matlab/tsa/
5 % $Id: content.m 5090 2008-06-05 08:12:04Z schloegl $
6 % Copyright (C) 1996-2003,2008 by Alois Schloegl <a.schloegl@ieee.org>
8 % Time Series Analysis - a toolbox for the use with Matlab
9 % aar adaptive autoregressive estimator
10 % acovf (*) Autocovariance function
11 % acorf (acf) (*) autocorrelation function
12 % pacf (*) partial autocorrelation function, includes signifcance test and confidence interval
13 % parcor (*) partial autocorrelation function
14 % biacovf biautocovariance function (3rd order cumulant)
16 % durlev (*) solves Yule-Walker equation - converts ACOVF into AR parameters
17 % lattice (*) calcultes AR parameters with lattice method
18 % lpc (*) calculates the prediction coefficients form a given time series
19 % invest0 (*) a prior investigation (used by invest1)
20 % invest1 (*) investigates signal (useful for 1st evaluation of the data)
21 % selmo (*) Select Order of Autoregressive model using different criteria
23 % hup (*) test Hurwitz polynomials
24 % ucp (*) test Unit Circle Polynomials
25 % y2res (*) computes mean, variance, skewness, kurtosis, entropy, etc. from data series
26 % ar_spa (*) spectral analysis based on the autoregressive model
27 % detrend (*) removes trend, can handle missing values, non-equidistant sampled data
28 % flix floating index, interpolates data for non-interger indices
29 % quantiles calculates quantiles
31 % Multivariate analysis (planned in future)
32 % mvar multivariate (vector) autoregressive estimation
33 % mvfilter multivariate filter
34 % arfit2 provides compatibility to ARFIT [Schneider and Neumaier, 2001]
36 % Conversions between Autocorrelation (AC), Autoregressive parameters (AR),
37 % prediction polynom (POLY) and Reflection coefficient (RC)
38 % ac2poly (*) transforms autocorrelation into prediction polynom
39 % ac2rc (*) transforms autocorrelation into reflexion coefficients
40 % ar2rc (*) transforms autoregressive parameters into reflection coefficients
41 % rc2ar (*) transforms reflection coefficients into autoregressive parameters
42 % poly2ac (*) transforms polynom to autocorrelation
43 % poly2ar (*) transforms polynom to AR
50 % sinvest1 shows the parameter calculated by INVEST1
53 % tsademo demonstrates INVEST1 on EEG data
54 % invfdemo demonstration of matched, inverse filtering
55 % bisdemo demonstrates bispectral estimation
57 % (*) indicates univariate analysis of multiple data series (each in a row) can be processed.
58 % (-) indicates that these functions will be removed in future
60 % REFERENCES (sources):
61 % http://www.itl.nist.gov/
62 % http://mathworld.wolfram.com/
63 % P.J. Brockwell and R.A. Davis "Time Series: Theory and Methods", 2nd ed. Springer, 1991.
64 % O. Foellinger "Lineare Abtastsysteme", Oldenburg Verlag, Muenchen, 1986.
65 % F. Gausch "Systemtechnik", Textbook, University of Technology Graz, 1993.
66 % M.S. Grewal and A.P. Andrews "Kalman Filtering" Prentice Hall, 1993.
67 % S. Haykin "Adaptive Filter Theory" 3ed. Prentice Hall, 1996.
68 % E.I. Jury "Theory and Application of the z-Transform Method", Robert E. Krieger Publishing Co., 1973.
69 % M.S. Kay "Modern Spectal Estimation" Prentice Hall, 1988.
70 % Ch. Langraf and G. Schneider "Elemente der Regeltechnik", Springer Verlag, 1970.
71 % S.L. Marple "Digital Spetral Analysis with Applications" Prentice Hall, 1987.
72 % C.L. Nikias and A.P. Petropulu "Higher-Order Spectra Analysis" Prentice Hall, 1993.
73 % M.B. Priestley "Spectral Analysis and Time Series" Academic Press, 1981.
74 % T. Schneider and A. Neumaier "Algorithm 808: ARFIT - a matlab package for the estimation of parameters and eigenmodes of multivariate autoregressive models"
75 % ACM Transactions on Mathematical software, 27(Mar), 58-65.
76 % C.E. Shannon and W. Weaver "The mathematical theory of communication" University of Illinois Press, Urbana 1949 (reprint 1963).
77 % W.S. Wei "Time Series Analysis" Addison Wesley, 1990.
80 % REFERENCES (applications):
81 % [1] A. Schlögl, B. Kemp, T. Penzel, D. Kunz, S.-L. Himanen,A. Värri, G. Dorffner, G. Pfurtscheller.
82 % Quality Control of polysomnographic Sleep Data by Histogram and Entropy Analysis.
83 % Clin. Neurophysiol. 1999, Dec; 110(12): 2165 - 2170.
84 % [2] Penzel T, Kemp B, Klösch G, Schlögl A, Hasan J, Varri A, Korhonen I.
85 % Acquisition of biomedical signals databases
86 % IEEE Engineering in Medicine and Biology Magazine 2001, 20(3): 25-32
89 % - Multiple Signal Processing
90 % - Efficient algorithms
91 % - Model order selection tools
92 % - higher (3rd) order analysis
93 % - Maximum entropy spectral estimation
94 % - can deal with missing values (NaN's)